New ToastHost website not showing up in search engine

Just wanted to thank you for your help on this issue. I would just like to confirm the following: Given our domain name registrar is redirecting the traffic from our old website this means that when the old site is taken down this will have no bearing whatsoever. All we need to do is ensure is that we continue to renew our domain name.
Thank you

Wrong, you need to get all references to the old domain changed to the new domain as soon as possible. Once the old domain stops forwarding you loose all traffic going to that address.